3. Titanic Corp issued 7 year 8% bonds due 2026 at par. This bond pays interest...

3. Titanic Corp issued 7 year 8% bonds due 2026 at par. This bond pays interest on a semi-annual basis. However, right after Titanic issued the bonds, the rate environment changed as the Fed lowered rates to stimulate growth. Now the market’s required return is 4% (all else being equal).

In this current environment, what is the trading price of the bond? Is this bond trading at a discount or premium? (5 points)

Now suppose you find out that Titanic bonds are callable in 2 years at 101% (or $1010) right after Titanic issued the bonds. Assuming the trading price you found above, what is the bond’s yield to call? Is the yield to call or yield to maturity higher? Why? (Hint: the yield to call is the yield you get if you hold the bond until the call date and redeem the call price ) (5 points)

Solutions

Expert Solution

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 4%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 7 * 2 (7 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,242.12

Trading price of the bond is $1,242.12. It is trading at a premium.

YTC is calculated using RATE function in Excel with these inputs :

nper = 2*2 (2 years to call date with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -1242.12 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1010 (call price of the bond receivable on call date. This is a positive figure as it is an inflow to the bondholder)

The RATE calculated is the semiannual YTC. To calculate the annual YTC, we multiply by 2. Annual YTC is -3.12%

The YTM is higher

jeff jeffy answered 1 year ago

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